Integral of arcctg(x+1) dx
The solution
The answer (Indefinite)
[src]
/ / 2\
| log\1 + (x + 1) /
| acot(x + 1) dx = C + ----------------- + (x + 1)*acot(x + 1)
| 2
/
$${{\log \left(\left(x+1\right)^2+1\right)}\over{2}}+\left(x+1\right)
\,{\rm arccot}\; \left(x+1\right)$$
log(5) log(2) pi
------ + 2*acot(2) - ------ - --
2 2 4
$${{\log 5-2\,\arctan 2+2\,\arctan \left({{1}\over{2}}\right)}\over{2
}}-{{2\,\log 2-\pi}\over{4}}$$
=
log(5) log(2) pi
------ + 2*acot(2) - ------ - --
2 2 4
$$- \frac{\pi}{4} - \frac{\log{\left(2 \right)}}{2} + \frac{\log{\left(5 \right)}}{2} + 2 \operatorname{acot}{\left(2 \right)}$$
Use the examples entering the upper and lower limits of integration.